Trigonometry - Previous Year IPM/BBA Questions

The best way to prepare for Trigonometry is by going through the previous year Trigonometry questions for IPMAT - Indore. Here we bring you all previous year Trigonometry IPMAT - Indore questions along with detailed solutions.

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1. IPMAT (I) 2023 QA MCQ | Trigonometry IPMAT - Indore Question

If cosα + cosβ = 1, then the maximum value of sinα – sinβ is

(a)
2
(b)
√2
(c)
1
(d)
√3

2. IPMAT (I) 2023 QA MCQ | Trigonometry IPMAT - Indore Question

If log_cosxsinx + log_sinxcosx = 2, then the value of x is

(a)
nπ/4 + π/4, n is an integer
(b)
2nπ + π/4, n is an integer
(c)
nπ + π/4, n is an integer
(d)
nπ/4, n is an integer

3. IPMAT (I) 2022 QASA | Trigonometry IPMAT - Indore Question

Sin α + Sin β = $\frac{\sqrt{2}}{\sqrt{3}}$ and Cos α + Cos β = $\frac{1}{\sqrt{3}}$ , then the value of ${(20 \cos (\frac{α - β}{2}))}^{2}$ is _______.

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Answer: 100

Text Explanation :

Sin α + Sin β = $\frac{\sqrt{2}}{\sqrt{3}}$ ...(1) and
Cos α + Cos β = $\frac{1}{\sqrt{3}}$ ...(2),

Squaring both the equations and adding them we get.

⇒ Sin² α + Sin² β + 2 × Sin α × Sin β + Cos² α + Cos² β + 2 × Cos α × Cos β = $\frac{2}{3}$ + $\frac{1}{3}$

⇒ Sin² α + Cos² α + Sin² β + Cos² β + 2 × Sin α × Sin β + 2 × Cos α × Cos β = 1

⇒ 1 + 1 + 2 × cos (α - β) = 1

⇒ cos (α - β) = - 1/2

⇒ 2 × ${(\cos (\frac{α - β}{2}))}^{2}$ - 1 = - 1/2

⇒ ${(\cos (\frac{α - β}{2}))}^{2}$ = 1/4

∴ 20² × ${(\cos (\frac{α - β}{2}))}^{2}$ = 400

⇒ ${(20 \cos (\frac{α - β}{2}))}^{2}$ = 100.

Hence, 100.

4. IPMAT (I) 2022 QA MCQ | Trigonometry IPMAT - Indore Question

For 0 < θ < π/4, let a = ((sinθ)^sinθ)(log₂cosθ), b = ((cosθ)^sinθ)(log₂sinθ), c = ((sinθ)^cosθ)(log₂cosθ) and d = ((sinθ)^sinθ)(log₂sinθ). Then, the median value in the sequence a, b, c, d is

(a)
(a + b)/2
(b)
(a + d)/2
(c)
(b + c)/2
(d)
(c + d)/2

5. IPMAT (I) 2022 QA MCQ | Trigonometry IPMAT - Indore Question

The curve represented by the equation $\frac{x^{2}}{\sin \sqrt{2} - \sin \sqrt{3}}$ + $\frac{y^{2}}{c o s \sqrt{2} - c o s \sqrt{3}}$ = 1 is

(a)
an ellipse with the foci on the y-axis
(b)
an ellipse with the foci on the x-axis
(c)
a hyperbola with the foci on the x-axis
(d)
a hyperbola with the foci on the y-axis

Answer: Option A

Text Explanation :

Equation $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ represents an ellipse.

Hence, the given curve is an ellipse. We need to figure out the foci of this ellipse.

Also, Cos√2 - cos√3 > Sin√2 - Sin√3 > 0

⇒ b² > a²

∴ Foci is on y-axis.

Hence, option (a).

6. IPMAT (I) 2022 QA MCQ | Trigonometry IPMAT - Indore Question

Ayesha is standing atop a vertical tower 200 m high and observes a car moving away from the tower on a straight, horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be 45°. At 11:02 AM, she observes the angle of depression of the car to be 30°. The speed at which the car is moving is approximately

(a)
6.3 km per hour
(b)
8.45 km per hour
(c)
10.6 km per hour
(d)
4.39 km per hour

Answer: Option D

Text Explanation :

At 11 am, the car is at C and Ayesha is at A.
In △ABC, angle ACB = 45°
Tan45° = 1 = $\frac{AB}{BC}$
⇒ BC = AB = 200

At 11:02 am, the car is at D and Ayesha is at A.
In △ABD, angle ADB = 30°
Tan30° = $\frac{1}{\sqrt{3}}$ = $\frac{AB}{BD}$
⇒ BD = AB√3 = 200√3

⇒ CD = 200√3 - 200 = 200(√3 - 1) = 200(0.732) = 146.4 m

∴ The car moved 146.4 m in 2 minutes.

⇒ Speed of the car = $\frac{0.1464 kms}{\frac{2}{60} hours}$ = 4.392 kmph.

Hence, option (d).

7. IPMAT (I) 2021 QA MCQ | Trigonometry IPMAT - Indore Question

The set of all real value of p for which the equation 3sin²x + 12cosx – 3 = p has at least one solution is

(a)
[-12, 12]
(b)
[-12, 9]
(c)
[-15, 9]
(d)
[-15, 12]

8. IPMAT (I) 2020 QA MCQ | Trigonometry IPMAT - Indore Question

The value of $\cos^{2} \frac{π}{8}$ + $\cos^{2} \frac{3 π}{8}$ + $\cos^{2} \frac{5 π}{8}$ + $\cos^{2} \frac{7 π}{8}$

(a)
1
(b)
3/2
(c)
2
(d)
9/4

Answer: Option C

Text Explanation :

Given, $\cos^{2} \frac{π}{8}$ + $\cos^{2} \frac{3 π}{8}$ + $\cos^{2} \frac{5 π}{8}$ + $\cos^{2} \frac{7 π}{8}$

= $\cos^{2} \frac{π}{8}$ + $\cos^{2} \frac{3 π}{8}$ + $\cos^{2} (\frac{π}{2} + \frac{π}{8})$ + $\cos^{2} (\frac{π}{2} + \frac{3 π}{8})$

= $\cos^{2} \frac{π}{8}$ + $\cos^{2} \frac{3 π}{8}$ + $\sin^{2} \frac{π}{8}$ + $\sin^{2} \frac{3 π}{8}$

= $\cos^{2} \frac{π}{8}$ + $\sin^{2} \frac{π}{8}$ + $\cos^{2} \frac{3 π}{8}$ + + $\sin^{2} \frac{3 π}{8}$

= 1 + 1 = 2

Hence, option (c).

9. IPMAT (I) 2019 QASA | Trigonometry IPMAT - Indore Question

The number of pairs (x, y) satisfying the equation sinx + siny = sin(x + y) and |x| + |y| = 1 is

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10. IPMAT (I) 2019 QA MCQ | Trigonometry IPMAT - Indore Question

Given that cos x + cos y = 1, the range of sin x - sin y is

(a)
[-1, 1]
(b)
[-2, 2]
(c)
[0, √3]
(d)
[-√3, √3]

11. IPMAT (I) 2019 QA MCQ | Trigonometry IPMAT - Indore Question

If sinθ + cosθ = m, then sin⁶θ + cos⁶θ equals

(a)
3(m² + 1)/4
(b)
3(m² - 1)/4
(c)
1 - 3(m² - 1)/4
(d)
1 - 3(m² - 1)²/4

Trigonometry - Previous Year IPM/BBA Questions

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